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E(x; – x) = Ex} - Nx and E(x; - x)(y; – y) = Ex,yi – Nxy (d) Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. Xi Yi 3 5 2 2 2 Σχ Ey: Eŷi = Ex,ê; = %3D

E(x; – x) = Ex} - Nx and E(x; - x)(y; – y) = Ex,yi – Nxy (d) Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. Xi Yi 3 5 2 2 2 Σχ Ey: Eŷi = Ex,ê; = %3D

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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please answer the question in the attached picture with work shown, thanks!

#1 D,E,F

Consider the following five observations. You are to do all the parts of this exercise using only a calculator. (x – x)? y - y (x – x) (y – y) y 3 3 ΣΧ Ey; E(x; – x) = E(xi – x)? = Σ-) - E(x; – x)(yi – y) = (a) Complete the entries in the table. Put the sums in the last row. What are the sample means and y? (b) Calculate bị and b2 using (27) and (28) and state their interpretation. (4) + lecture Notos, Ch.9 (5) (c) Compute E-1X, E-1xiyi. Using these numerical values, show that (x; – x)? = Ex} - Nx and E(x; - x)(y; – F) = Exy; – Nxy (d) Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. Xi Yi 3 5 2 2 2 Ex; = Eyi = Eŷi = E = Exiê; =
Transcribed Image Text:Consider the following five observations. You are to do all the parts of this exercise using only a calculator. (x – x)? y - y (x – x) (y – y) y 3 3 ΣΧ Ey; E(x; – x) = E(xi – x)? = Σ-) - E(x; – x)(yi – y) = (a) Complete the entries in the table. Put the sums in the last row. What are the sample means and y? (b) Calculate bị and b2 using (27) and (28) and state their interpretation. (4) + lecture Notos, Ch.9 (5) (c) Compute E-1X, E-1xiyi. Using these numerical values, show that (x; – x)? = Ex} - Nx and E(x; - x)(y; – F) = Exy; – Nxy (d) Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. Xi Yi 3 5 2 2 2 Ex; = Eyi = Eŷi = E = Exiê; =
Yi 3 2 3 2 2 Eỹi = Σ- Exiê; = %3D Plot the data points and sketch the fitted regression line (e) ŷi = bị + b2xi. (f) On the sketch in part (e), locate the point of the means (x, y). Does your fitted line pass through that point? If not, go back to the drawing board, literally. (g) Show that for these numerical values y = b1 + b2x. (h) Show that for these numerical values y = y, where ŷ = Eŷi/N. (i) Compute ô?. (j) Compute var(b2).
Transcribed Image Text:Yi 3 2 3 2 2 Eỹi = Σ- Exiê; = %3D Plot the data points and sketch the fitted regression line (e) ŷi = bị + b2xi. (f) On the sketch in part (e), locate the point of the means (x, y). Does your fitted line pass through that point? If not, go back to the drawing board, literally. (g) Show that for these numerical values y = b1 + b2x. (h) Show that for these numerical values y = y, where ŷ = Eŷi/N. (i) Compute ô?. (j) Compute var(b2).
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